Multistage Open-Shop-Problem: Schedules for N Tasks on K Machines with Different Technical Characteristics for an Arbitrary order of Tasks

The statements and mathematical models of the open — shop-problem are considered: performing N tasks on K machines with an arbitrary order of processing each task on all machines. Unlike most publications on solving this problem, the task posed is solved in a multi-stage formulation under the conditions of a sequential chain of sections and workshops of the enterprise, as well as in the presence of restrictions on the start and end times of tasks and the permissible operating times of machines. In addition, for scheduling systems of enterprises, it is extremely important to consider this task in a multi-stage setting, i.e. in a sequential chain of plots and workshops. The properties of admissible and optimal schedules, as well as algorithms of exact and approximate methods for solving these problems by successive optimization algorithms are investigated. At the early stages of solving the problem, the fact of incompatibility of the system of constraints of the task and the definition of a subset of tasks or resources, the time range of which should be expanded, is established. The described algorithms for solving the problem are illustrated by numerical examples.